Circular MotionHard
Question
A flyweel rotates about an axis. Due to friction at the axis, it experiences an angular retadation proportional to its angular velocity. If its angular velocity falls to half while it makes n rotations, how many more rotations will it make before coming to rest?
Options
A.2n
B.n
C.n/2
D.n/3
Solution
α is proportional to ω
let α = kω (∴ k is a constant)
= kω 
∴
kω ⇒ = kdθ
Now
dω = k∫dθ
dω = k 
dθ ⇒ - 
= kθ ⇒ - = kθ1
(∵ θ1 = 2πn)
∴ θ = θ1 or 2πn1 = 2πn
n1 = n
let α = kω (∴ k is a constant)
= kω ∴
kω ⇒ = kdθ Now
dω = k∫dθ dω = k dθ ⇒ - = kθ ⇒ - = kθ1(∵ θ1 = 2πn)
∴ θ = θ1 or 2πn1 = 2πn
n1 = n
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